He didn't "play" poems. He played in plays, some of which he wrote himself, and others which were written by others, including comedies, including "city comedies" like Every Man in his Humour by Ben Jonson, and "tragicomedies", as popularized by Beaumont and Fletcher, like his own The Winter's Tale, tragedies, and histories. His theatre company didn't play much in the pastoral genre, although As You Like It comes close.Shakespeare wrote poems also, both to be sold publicly (like Venus and Adonis) or to be shared privately (like the sonnets). They were not for performance.